Skip to main content

The continuity axiom and the Čech homology

  • Conference paper
  • First Online:
Geometric Topology and Shape Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1283))

This paper is in final form and no version of it will be submitted for publication elsewhere.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P. Bacon, Axioms for the Cech cohomology of paracompacta, Pacific J. Math. 52(1974) 7–9.

    Article  MathSciNet  MATH  Google Scholar 

  2. —, Continuous functors, General Topology Appl. 5(1975) 321–331.

    Article  MathSciNet  MATH  Google Scholar 

  3. G.E. Bredon, Sheaf theory, MaGraw-Hill Book Company, 1967.

    Google Scholar 

  4. C.E. Capel, Inverse limit spaces, Duke Math. J. 21(1954) 233–245.

    Article  MathSciNet  MATH  Google Scholar 

  5. S. Deo, On the tautness property of Alexander-Spanier cohomology, Proc. Amer. Math. Soc. 52(1975) 441–444.

    Article  MathSciNet  MATH  Google Scholar 

  6. S. Eilenberg and N. Steenrod, Foundations of algebraic topology, Princeton, New Jersey, Princeton Univ. Press, 1952.

    Book  MATH  Google Scholar 

  7. R. Godement, Topologie algébrique et théorie des faisceaux, Hermann, Paris, 1958.

    MATH  Google Scholar 

  8. S.T. Hu, Theory of retracts, Wayne State Univ. Press, Detroit, 1965.

    MATH  Google Scholar 

  9. J.D. Lawson, Comparison of taut cohomologies, Aequationes Math. 9(1973) 201–209.

    Article  MathSciNet  MATH  Google Scholar 

  10. C.N. Lee and F. Raymond, Čech extensions for contravariant functors, Trans. Math. Soc. 133(1968) 415–434.

    MathSciNet  MATH  Google Scholar 

  11. S. Mardešić, Approximate polyhedra, resolutions of maps and shape fibrations, Fund. Math. 114(1981) 53–78.

    MathSciNet  MATH  Google Scholar 

  12. —, On resolutions for pairs of spaces, Tsukuba J. Math. 8(1984) 81–93.

    MathSciNet  MATH  Google Scholar 

  13. —, On the homotopy type of ANRs for p-paracompacta, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 27(1979) 803–808.

    MathSciNet  MATH  Google Scholar 

  14. — and J. Segal, Shape theory, the inverse system approach, North-Holland Publishing Company, Amsterdam, 1982.

    MATH  Google Scholar 

  15. E. Michael, A note on paracompact spaces, Proc. Amer. Math. Soc. 4(1953) 831–838.

    Article  MathSciNet  MATH  Google Scholar 

  16. J. Milnor, On axiomatic homology theory, Pacific J. Math. 12(1962) 337–341.

    Article  MathSciNet  MATH  Google Scholar 

  17. —, On the Steenrod homology theory, Univ. of California, Berkeley, CA 1960 (mimeographed).

    MATH  Google Scholar 

  18. K. Morita, On shapes of topological spaces, Fund. Math. 86(1975) 251–259.

    MathSciNet  MATH  Google Scholar 

  19. —, Čech cohomology and covering dimension for topological spaces, Fund. Math. 87(1975) 31–52.

    MathSciNet  MATH  Google Scholar 

  20. K. Nagami, Dimension theory, Academic Press, New York, 1970.

    MATH  Google Scholar 

  21. S.V. Petkova, On the axioms of homology theory, Math. Sbornik, 90(1973) 607–624 = Math. USSR Sbornik 19(1973) 597–614.

    MathSciNet  Google Scholar 

  22. E.G. Skljarenko, Homology theory and the exactness axiom, Uspekhi Math. Nauk 245(1969) 87–140 = Russian Math. Surveys 24(1969) 91–142.

    MathSciNet  Google Scholar 

  23. —, Uniqueness theorems in homology theory, Math. Sbornik, 85(1971) 201–223 = Math. USSR Sbornik, 14(1971) 199–218.

    MathSciNet  Google Scholar 

  24. E.H. Spanier, Algebraic topology, MaGraw-Hill Book Company, Inc., New York, 1966.

    MATH  Google Scholar 

  25. —, Tautness for Alexander-Spanier cohomology, Pacific J. Math. 75(1978) 561–563.

    Article  MathSciNet  MATH  Google Scholar 

  26. N.E. Steenrod, Regular cycles of compact metric spaces, Ann. of Math. (2) 41(1940) 833–851.

    Article  MathSciNet  MATH  Google Scholar 

  27. K.A. Stinikov, Combinatorial topology of nonclosed sets I. The first duality law; spectral duality, Math. Sb. N. S. 34(1954) 3–54 = Amer. Math. Soc. Transl. (2)15(1960) 245–295.

    MathSciNet  Google Scholar 

  28. A.D. Wallace, The map excision theorem, Duke Math. J. 19(1952) 177–182.

    Article  MathSciNet  MATH  Google Scholar 

  29. T. Watanabe, Approximative expansions of maps into inverse systems, to appear in Proc. of Banach Math. Center.

    Google Scholar 

  30. —, Čech homology, Steenrod homology and strong homology I, to appear in Glasnik Mat.

    Google Scholar 

  31. —, Approximative Shape I-IV, to appear in Tsukuba J. Math.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Sibe Mardešić Jack Segal

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag

About this paper

Cite this paper

Watanabe, T. (1987). The continuity axiom and the Čech homology. In: Mardešić, S., Segal, J. (eds) Geometric Topology and Shape Theory. Lecture Notes in Mathematics, vol 1283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081431

Download citation

  • DOI: https://doi.org/10.1007/BFb0081431

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18443-0

  • Online ISBN: 978-3-540-47975-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics